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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 354900.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 354900.dn1 | 354900dn1 | \([0, 1, 0, -2388533, 1420001688]\) | \(1248870793216/42525\) | \(51315013181250000\) | \([2]\) | \(6220800\) | \(2.2981\) | \(\Gamma_0(N)\)-optimal |
| 354900.dn2 | 354900dn2 | \([0, 1, 0, -2282908, 1551399188]\) | \(-68150496976/14467005\) | \(-279317879748180000000\) | \([2]\) | \(12441600\) | \(2.6447\) |
Rank
sage: E.rank()
The elliptic curves in class 354900.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 354900.dn do not have complex multiplication.Modular form 354900.2.a.dn
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
